[tex]a) 6;54\\m_a=\frac{a+b}{2} =\frac{6+54}{2} =\frac{60}{2} =30\\m_g=\sqrt{a*b} =\sqrt{6*54} =\sqrt{6} *3\sqrt{6} =3*6=18\\18<30 =>m_g\leq m_a[/tex]
[tex]b)\frac{1}{4} ;\frac{1}{9} \\m_a=\frac{\frac{1}{4} +\frac{1}{9} }{2} =\frac{\frac{9}{36}+\frac{4}{36} }{2} \\m_a=\frac{\frac{13}{36} }{2} =\frac{13}{36} *\frac{1}{2} =\frac{13}{72} \\m_g=\sqrt{\frac{1}{4} *\frac{1}{9} } =\frac{1}{2} *\frac{1}{3} =\frac{1}{6} \\\frac{1}{6} =\frac{6}{36} =\frac{12}{72} \\=>\frac{12}{72} <\frac{13}{72} =>m_g\leq m_a[/tex]
[tex]c) 5; 7,2\\m_a=\frac{a+b}{2} =\frac{5+7,2}{2} =\frac{12,2}{2} =6,1\\m_g=\sqrt{5*7,2} =\sqrt{36} =6\\6<6,1=>m_g\leq m_a[/tex]
[tex]d)\sqrt{2} ;\sqrt{8} \\m_a=\frac{a+b}{2} =\frac{\sqrt{2}+\sqrt{8} }{2} =\frac{\sqrt{2} +2\sqrt{2} }{2} =\frac{3\sqrt{2} }{2} =1,5\sqrt{2} \\m_g=\sqrt{a*b} =\sqrt{\sqrt{2}*\sqrt{8} } =\sqrt{\sqrt{16} } =\sqrt{4} =2\\1,5\sqrt{2} =\sqrt{(1,5)^2*2} =\sqrt{2,25*2} =\sqrt{4,5} \\2=\sqrt{4} \\=>\sqrt{4} <\sqrt{4,5} =>2<1,5\sqrt{2} =>m_g\leq m_a[/tex]
[tex]e) 25\sqrt{3} ;12\sqrt{3} \\m_a=\frac{a+b}{2} =\frac{25\sqrt{3} +12\sqrt{3} }{2} =\frac{37\sqrt{3} }{2} =18,5\sqrt{3} \\m_g=\sqrt{a*b} =\sqrt{25\sqrt{3} *12\sqrt{3} } \\=\sqrt{25*12*3} =\sqrt{5*5*4*3*3} \\=5*2/*3=30\\30=\sqrt{900} \\18,5\sqrt{3} =\sqrt{(18,5)^2*3} =\sqrt{342,25*3} =\sqrt{1026,75} \\\sqrt{900} <\sqrt{1026,75} =>30<18,5\sqrt{3} =>m_g\leq m_a[/tex]
[tex]f)1\frac{1}{7} ;\frac{3}{125} \\m_a=\frac{a+b}{2} =\frac{1\frac{1}{7}+\frac{3}{125} }{2} =\frac{\frac{8}{7} +\frac{3}{125} }{2} =aprox0,58\\=\frac{\frac{1000}{875} +\frac{21}{875} }{2} =\frac{\frac{1021}{875} }{2} =\\=\frac{1021}{875} *\frac{1}{2} =\frac{1021}{1750} =\\m_g=\sqrt{\frac{8}{7}*\frac{3}{125} } =\sqrt{\frac{24}{875} } =\frac{2\sqrt{6} }{5\sqrt{35} } =\frac{2\sqrt{210} }{175} =aprox0,16\\0,16<0,58=>\frac{2\sqrt{210} }{175} <\frac{1021}{1750} =>m_g\leq m_a[/tex]
